Perceptual grouping organizes image parts in clusters based on psychophysically plausible similarity measures. We propose a novel grouping method in this paper, which stresses connectedness of image elements via mediating elements rather than favoring high mutual similarity. This grouping principle yields superior clustering results when objects are distributed on low-dimensional extended manifolds in a feature space, and not as local point clouds. In addition to extracting connected structures, objects are singled out as outliers when they are too far away from any cluster structure. The objective function for this perceptual organization principle is optimized by a fast agglomerative algorithm. We report on perceptual organization experiments where small edge elements are grouped to smooth curves. The generality of the method is emphasized by results from grouping textured images with texture gradients in an unsupervised fashion.